In this work, we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p>2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi (Boll. U.M.I. (4) 11(Suppl. fasc. 3): 1-32, 1975), using the new definition of nondegeneracy given in (Cingolani- Vannella, Ann. Inst. H. Poincaré: Analyse Non Linéaire. 20:271-292, 2003). We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini (Nonlinear Anal. T.M.A. 12:761-775, 1988) in the Hilbert case, to our Banach setting.
Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces / Cingolani, Silvia; Vannella, Giuseppina. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 186:1(2007), pp. 157-185. [10.1007/s10231-005-0176-2]
Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces
CINGOLANI, Silvia;VANNELLA, Giuseppina
2007-01-01
Abstract
In this work, we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p>2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi (Boll. U.M.I. (4) 11(Suppl. fasc. 3): 1-32, 1975), using the new definition of nondegeneracy given in (Cingolani- Vannella, Ann. Inst. H. Poincaré: Analyse Non Linéaire. 20:271-292, 2003). We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini (Nonlinear Anal. T.M.A. 12:761-775, 1988) in the Hilbert case, to our Banach setting.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
